Application of Multichannel Scattering Theory to Pionic Reactions Within the Lee Model

The multichannel scattering theory is applied to the (2,2) sector of the (non-static) Lee model. Rigorous expressions for the transition amplitudes for two-fragments channels are derived. These expressions contain all effects of off-shell renormalization in a complete and consistent way. With suitable identification of the elementary fields of the model the reactions considered correspond to a simplified description of elastic proton-proton and pion-deuteron scattering and to pion absorption on the deuteron. We obtain a two-body equation for the description of the elastic proton-proton scattering and an extension of the two-potential formula for the pion-deuteron scattering, which can be cast into the form of the multiple-scattering series.